78.12.1 problem 1 (a)

Internal problem ID [18288]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 1 (a)
Date solved : Tuesday, January 28, 2025 at 11:45:13 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)+diff(y(x),x)-6*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_{1} {\mathrm e}^{5 x}+c_{2} \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}] +D[y[x],x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (c_2 e^{5 x}+c_1\right ) \]